Year: 2021
Author: Zhenwei Zhang, Xue Li, Huibin Chang, Zhenwei Zhang, Yuping Duan, Huibin Chang, Yuping Duan
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1017–1041
Abstract
We concern with fast domain decomposition methods for solving the total variation minimization problems in image processing. By decomposing the image domain into non-overlapping subdomains and interfaces, we consider the primal-dual problem on the interfaces such that the subdomain problems become independent problems and can be solved in parallel. Suppose both the interfaces and subdomain problems are uniformly convex, we can apply the acceleration method to achieve an $\mathcal{O}(1 / n^2)$ convergent domain decomposition algorithm. The convergence analysis is provided as well. Numerical results on image denoising, inpainting, deblurring, and segmentation are provided and comparison results with existing methods are discussed, which not only demonstrate the advantages of our method but also support the theoretical convergence rate.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0146
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1017–1041
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Non-overlapping domain decomposition method primal-dual algorithm total variation Rudin-Osher-Fatemi model Chan-Vese model.